UC Irvine

The random-phase approximation (RPA) incorporates many appealing features absent in semilocal density functional theory (DFT) without excessively increasing computational cost. The first half of this thesis addresses the question: Can one achieve a similar balance between accuracy and speed for beyond-RPA corrections? To this end, low-scaling algorithms are developed for the most common perturbative corrections to RPA, including the bare second-order exchange (SOX), second-order screened exchange (SOSEX), and approximate exchange kernel (AXK) methods. The implementations are based on the resolution-of-the-identity (RI) approximation, Clenshaw-Curtis numerical frequency quadrature, and optionally, integral prescreening. These implementations afford benchmark calculations on medium- and large-size molecules with size-independent accuracy. The benchmark results show that the AXK method systematically improves RPA and surpasses SOX and SOSEX for reaction barrier heights, reaction energies, and noncovalent interaction energies of main-group compounds, confirming conclusions drawn from previous small-molecule calculations.The superior accuracy of AXK compared with SOX and SOSEX suggests that the strong screening of bare SOX in AXK is important. Nevertheless, benchmark calculations on 3d transition metal compounds show that RPA and its perturbative corrections eventually break down for systems with strong static correlation, such as metal dimers. The reliability of RPA methods can be estimated using an effective coupling strength α̅ proposed herein. The second half of the thesis demonstrates the use of electronic structure methods for the identification and characterization of {Sc[N(SiMe₃)₂]₃}⁻, {[(R₂N)₃Sc]₂}[μ-η¹:η¹-N₂]}²⁻, and {Pu[C₅H₃(SiMe₃)₂]₃}⁻: DFT and time-dependent DFT calculations played an important role in characterizing the electron configurations, bonding, and UV-visible spectroscopy of these unconventional rare-earth and actinide compounds. The applicability of RPA and AXK to these compounds is assessed, using the Pu²⁺ complex as an example.